# XDI analysis of Mutual-Exclusion Element

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```Processing AND/IF input stream:
-----------------------------------------------------------------------------
1> (AND/IF_1.0
2>   (NFA
3>     (NAME Mutual-Exclusion Element)
4>     (SYMBOLS
5>       (r0 INPUT) (a0 OUTPUT) (r1 INPUT) (a1 OUTPUT)
6>     )
7>
8>     (STATES
9>       (0 INITIAL BOX)
10>       (1 TRANSIENT)
11>       (4 TRANSIENT)
12>       (2 BOX)
13>       (5 TRANSIENT)
14>       (3 TRANSIENT)
15>       (6 BOX)
16>       (7 TRANSIENT)
17>       (8 BOX)
18>       (9 BOX)
19>       (10 TRANSIENT)
20>       (11 TRANSIENT)
21>       (12 TRANSIENT)
22>       (14 TRANSIENT)
23>       (13 TRANSIENT)
24>     )
25>     (TRANSITIONS
26>       (0 1 r0) (0 4 r1)
27>       (1 2 a0) (1 5 r1)
28>       (4 5 r0) (4 8 a1)
29>       (2 3 r0) (2 6 r1)
30>       (5 6 a0) (5 9 a1)
31>       (3 0 a0) (3 7 r1)
32>       (6 7 r0)
33>       (7 4 a0) (7 10 a1)
34>       (8 9 r0) (8 11 r1)
35>       (9 12 r1)
36>       (10 8 a0) (10 14 r1)
37>       (11 12 r0) (11 0 a1)
38>       (12 13 a0) (12 1 a1)
39>       (14 11 a0) (14 3 a1)
40>       (13 14 r0) (13 2 a1)
41>     )
42>   )
43> )
-----------------------------------------------------------------------------

Mutual-Exclusion Element: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Mutual-Exclusion Element: 1 warning, 0 errors.

```

### Statistics

4 symbols:
2 input and 2 output
15 states:
0 demanding, 5 indifferent and 10 transient
28 transitions:
14 input and 14 output
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### Automorphisms (symmetries)

There are 2 automorphisms.
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### Finest Semi-independent Partition

/ r0 a0 / r1 a1 /
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### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Zinp)
• Disabling outputs (Zout) in state(s):
5
• Order-Independent input (Yinp)
• Order-Independent output (Yout)
• Output refusal sets do NOT propagate backward over inputs in state(s):
1 4
• Output Non-Deterministic
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### Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]
11111
014253678901243
0:011223342353465

Initial state reachable from all states.
All states reachable from all other states.

Shortest paths from initial state:
 0: r0 r1 r0 a0 r0 r1 r0 a0 r0 r0 a0 r1 r0 a0 r0 r1 r1 a1 r0 r1 a1 r0 a0 r0 r1 a1 r1 a1 r1 r0 r1 a1 r1 r0 a0 r0 r1 a1 r1 r0 r1 a1 r1 a0

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[ c]
0:11]
1:23]
2:36]
3:4[10]
4:2[12]
5:2[14]
6:1[15]
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### Autocomparison Matrix

There are no state pairs (x,y) where x refines y outside the diagonal.

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### XDI Validity

'Mutual-Exclusion Element' is a valid XDI specification.

Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

XDI State Graph Tool, Version 2.0 (Feb 17 1998 20:34:43)